*Giacomo Albi, Michael Herty, Lorenzo Pareschi*

(30/01/2014

*Communications in Mathematical Sciences*, 13 (2015)

1407 – 1429, arXiv:1401.7798)

In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a Boltzmann-type equation based on a model predictive control formulation is introduced and discussed.

In particular, the receding horizon strategy permits to embed the minimization of suitable cost functional into binary particle interactions. The corresponding Fokker-Planck asymptotic limit is also derived and explicit expressions of stationary solutions are given. Several numerical results showing the robustness of the present approach are finally reported.